Modeling of Whispering Gallery Modes for Rare Earth Spectroscopic Characterization

Abstract

A refined model of a mid-IR amplifier, constituted by a tapered chalcogenide fiber coupled to an erbium-doped chalcogenide microsphere, is integrated with a global solution search procedure based on particle swarm optimization approach. It is implemented in a computer code in order to obtain an inversion algorithm useful to evaluate the spectroscopic parameters of rare-earth-doped glass microspheres. The rare earth parameters can be recovered by means of the optical gain measurement. The error in evaluation of the erbium lifetime τ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">41</sub> is <;3.5%. It is <;0.5% for the other lifetimes and ion-ion interaction parameters. These excellent results are obtained since whispering gallery mode electromagnetic field interacts with rare earth for long effective distances.